Connecticut, like most states, does not treat all candidates equally, on the matter of ballot position. Major party nominees are automatically placed in the best spots on the ballot; then come previously qualified minor parties; then new parties; then independent candidates.
A minority of states, including all states in the 8th circuit, do give each party and each candidate an equal opportunity to appear on the best spot on the ballot. Courts outside the 8th circuit, for the most part, have refused to rule discriminatory ballot placement laws unconstitutonal, on the absurd grounds that it doesn’t make any difference.
News reports from the Connecticut U.S. Senate race make it clear that everyone in Connecticut who follows this issue does believe that ballot placement makes a difference in that race. There is speculation that the Republican nominee for U.S. Senate, who will enjoy the best spot on the ballot (because the Republican Party won the 2002 gubernatorial election) will get an advantage from his ballot position. There is also consensus that Senator Lieberman will suffer from appearing 6th on the ballot, behind the lines reserved for the Democratic, Republican, Green, Constitution and Libertarian Parties (there is no Libertarian on the ballot for US Senate, but there are Libertarians on the ballot for certain other statewide offices, so in towns using the party-column style, a blank Libertarian square will appear above Lieberman).
Also, in certain legislative districts in Connecticut, as well as one congressional district, the Working Families Party is a ballot-qualified party for those district offices, and it will also appear above Lieberman, even though it also lacks a U.S. Senate candidate.